#### Answer

$\color{blue}{(D' \cap U) \cup E = \left\{3, 4, 5, 6, 7, 8, 9, 10\right\}}$

#### Work Step by Step

RECALL:
(1) $\cup$ represents the union of sets, which is the set that contains the combined elements of the sets involved.
(2) $\cap$ represents the intersection of sets, which is the set that contains the elements common to the sets involved.
(3) $A'$ represents the complement of $A$, which is the set that contains the elements of the universal set $U$ that are not in $A$>
Given:
$D=\left\{1, 2, 3\right\}$
$E=\left\{3, 7\right\}$
$U=\left\{1, 2, 3, 4, 5, 6, 7, 8, 9, 105\right\}$
Thus,
$D'=\left\{4, 5, 6, 7, 8,9, 10\right\}$
The intersection of the universal set and any of its subset is the subset itself.
Thus,
$D'\cap U=D'=\left\{4, 5, 6, 7, 8, 9, 10\right\}$
Combining the elements of the set above and the set $E$ gives:
$\color{blue}{(D' \cap U) \cup E = \left\{3, 4, 5, 6, 7, 8, 9, 10\right\}}$